A221531 Triangle read by rows: T(n,k) = A000005(n-k+1)*A000041(k-1), n>=1, k>=1.

1, 2, 1, 2, 2, 2, 3, 2, 4, 3, 2, 3, 4, 6, 5, 4, 2, 6, 6, 10, 7, 2, 4, 4, 9, 10, 14, 11, 4, 2, 8, 6, 15, 14, 22, 15, 3, 4, 4, 12, 10, 21, 22, 30, 22, 4, 3, 8, 6, 20, 14, 33, 30, 44, 30, 2, 4, 6, 12, 10, 28, 22, 45, 44, 60, 42, 6, 2, 8, 9, 20, 14, 44, 30, 66, 60, 84, 56

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Formula

T(n,k) = d(n-k+1)*p(k-1), n>=1, k>=1.

Example

For n = 6:
-------------------------
k   A000041        T(6,k)
1      1  *  4   =    4
2      1  *  2   =    2
3      2  *  3   =    6
4      3  *  2   =    6
5      5  *  2   =   10
6      7  *  1   =    7
.         A000005
-------------------------
So row 6 is [4, 2, 6, 6, 10, 7]. Note that the sum of row 6 is 4+2+6+6+10+7 = 35 equals A006128(6).
.
Triangle begins:
1;
2,  1;
2,  2,  2;
3,  2,  4,  3;
2,  3,  4,  6, 5;
4,  2,  6,  6, 10, 7;
2,  4,  4,  9, 10, 14, 11;
4,  2,  8,  6, 15, 14, 22, 15;
3,  4,  4, 12, 10, 21, 22, 30, 22;
4,  3,  8,  6, 20, 14, 33, 30, 44, 30;
2,  4,  6, 12, 10, 28, 22, 45, 44, 60, 42;
6,  2,  8,  9, 20, 14, 44, 30, 66, 60, 84, 56;
...

Crossrefs

Mirror of A221530. Columns 1-3: A000005, A000005, A062011. Leading diagonals 1-2: A000041, A139582. Row sums give A006128.

Cf. A140207, A182703.

Sequence in context: A261679 A147657 A029232 * A282970 A025807 A120254

Adjacent sequences: A221528 A221529 A221530 * A221532 A221533 A221534

Keyword

nonn,tabl

Author

Omar E. Pol, Jan 19 2013

Status

approved